So why exactly does forward euler cause an increase in energy and backward euler cause a dampening?

dvanmali

The concept of forward Euler theoretically should would and not create an increase or decrease in Energy. If we were to use this same equation but instead add a cap to the minimum and maximum, can this solve the forward Euler problem? Is there a mathematical proof why this extra energy comes, because it has to come from somewhere (ie double value overflow, rounding errors, max-min)

keenan

@merc Check out the slides on "stability analysis" in this slide deck, and feel free to ask again if something still isn't clear!

keenan

@dvanmali Likewise, check out the next slide, which shows why forward Euler blows up. You could try artificially capping the velocity (say) to a maximum/minimum value, but this will generally yield motion that can look totally wrong. (You might even try it for A4!)

So why exactly does forward euler cause an increase in energy and backward euler cause a dampening?

The concept of forward Euler theoretically should would and not create an increase or decrease in Energy. If we were to use this same equation but instead add a cap to the minimum and maximum, can this solve the forward Euler problem? Is there a mathematical proof why this extra energy comes, because it has to come from somewhere (ie double value overflow, rounding errors, max-min)

@merc Check out the slides on "stability analysis" in this slide deck, and feel free to ask again if something still isn't clear!

@dvanmali Likewise, check out the next slide, which shows why forward Euler blows up. You could try artificially capping the velocity (say) to a maximum/minimum value, but this will generally yield motion that can look totally wrong. (You might even try it for A4!)